Model for large-area monolayer coverage of polystyrene nanospheres by spin coating

Nanosphere lithography, an inexpensive and high throughput technique capable of producing nanostructure (below 100 nm feature size) arrays, relies on the formation of a monolayer of self-assembled nanospheres, followed by custom-etching to produce nanometre size features on large-area substrates. A theoretical model underpinning the self-ordering process by centrifugation is proposed to describe the interplay between the spin speed and solution concentration. The model describes the deposition of a dense and uniform monolayer by the implicit contribution of gravity, centrifugal force and surface tension, which can be accounted for using only the spin speed and the solid/liquid volume ratio. We demonstrate that the spin recipe for the monolayer formation can be represented as a pathway on a 2D phase plane. The model accounts for the ratio of polystyrene nanospheres (300 nm), water, methanol and surfactant in the solution, crucial for large area uniform and periodic monolayer deposition. The monolayer is exploited to create arrays of nanoscale features using 'short' or 'extended' reactive ion etching to produce 30-60 nm (diameter) nanodots or 100-200 nm (diameter) nanoholes over the entire substrate, respectively. The nanostructures were subsequently utilized to create master stamps for nanoimprint lithography.